Allen John-Mark A, Cross M C
Corpus Christi College, University of Cambridge, Cambridge, CB2 1RH, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):052902. doi: 10.1103/PhysRevE.87.052902. Epub 2013 May 8.
Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be independent of N for large N, unlike the case of purely dissipative coupling where the improvement is proportional to N, but instead depends on just those oscillators in the core of the spiral that acts as the source region of the waves. Our conclusions are based on numerical simulations of up to N=29929 oscillators and analytic results for a continuum approximation to the lattice in an infinite system. We derive an expression for the dependence of the frequency precision on the reactive component of the coupling constant, depending on a single parameter given by fitting the frequency of the spiral waves to the numerical simulations.
在形成螺旋图案的情况下，具有反应性耦合的N个同步振荡器的二维晶格被视为高精度频率源。结果表明，对于大的N，频率精度的提高与N无关，这与纯耗散耦合的情况不同，在纯耗散耦合中，精度提高与N成正比，而是仅取决于螺旋核心中作为波源区域的那些振荡器。我们的结论基于对多达 N = 29929 个振荡器的数值模拟以及无限系统中晶格连续近似的解析结果。我们推导了频率精度对耦合常数反应性分量的依赖表达式，该表达式取决于通过将螺旋波频率与数值模拟拟合得到的单个参数。
